# How do you solve the following system:  -8x+2y=4 , 2x+5y=-1 ?

May 16, 2018

$x = - \frac{1}{2} , y = 0$

#### Explanation:

$\therefore - 8 x + 2 y = 4 - - - - - - - \left(1\right)$

$\therefore 2 x + 5 y = - 1 - - - - - - - - \left(2\right)$

$\therefore \left(2\right) \times 4$

$\therefore 8 x + 20 y = - 4 - - - - - - - \left(3\right)$

$\therefore \left(1\right) + \left(3\right)$

$\therefore 22 y = 0$

$\therefore y = 0$

substitute $y = 0 \in \left(2\right)$

$\therefore 2 x + 5 \left(0 = - 1\right)$

$\therefore 2 x = - 1$

$\therefore x = - \frac{1}{2}$

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check:-

substitute $x = - \frac{1}{2}$ and $y = 0$ in $\left(1\right)$

$\therefore - 8 \left(- \frac{1}{2}\right) + 2 \left(0 = 4\right)$

$\therefore 4 + 0 = 4$

$\therefore 4 = 4$